Using Newton's 2nd law, show that all objects subject to the pull of gravity alone should fall at the same rate. What is that rate?

No chatgpt pls will upvote

A cart on wheels (assume frictionless) with a mass of 20 kg is pulled rightward with a 50N force.  What is its acceleration?

Light travels through a vacuum at a speed of 2.998 x 108m/s. Determine the speed of light in the following media: crown glass (n = 1.52)

2.62 Collision. The engineer of a passenger train traveling at 25.0 m/s sights a freight train whose caboose is 200 m ahead on the same track (Fig. P2.62). The freight train is traveling at 15.0 m/s in the same direction as the passenger train. The engineer of the passenger train immediately applies the brakes, causing a constant acceleration of 0.100 m/s² in a direction opposite to the train's velocity, while the freight train continues with constant speed. Take x = 0 at the location of the front of the passenger train when the engineer applies the brakes. (a) Will the cows nearby witness a collision? (b) If so, where will it take place? (c) On a single graph, sketch the positions of the front of the pas- senger train and the back of the freight train.

Can I get help with how to calculate total displacement? The answer is 78.3x-4.8y

2.70 Egg Drop. You are on the Figure P2.70 roof of the physics building, 46.0 m above the ground (Fig. P2.70). Your physics professor, who is 1.80 m tall, is walking alongside the building at a constant speed of 1.20 m/s. If you wish to drop an egg on your profes- sor's head, where should the profes- sor be when you release the egg? Assume that the egg is in free fall. 2.71 CALC The acceleration of a particle is given by ax(t) = -2.00 m/s² +(3.00 m/s³)t. (a) Find the initial velocity Vox such that v = 1.20 m/s 1.80 m 46.0 m

One has to push down a ball with a force of 470 Newtons in order to hold the ball still, completely submerged under the surface of the water. What is the volume of the styrofoam ball in cubic meters? Use 997 kg/m3 as the density of water, 95 kg/m3 for the density of the styrofoam, and g = 9.8 m/s2.

The cube is placed in a bucket of water and find that it floats, with 33% of its volume submerged below the surface of the water. What is the density of the mystery material? The material is uniformly distributed throughout the solid cube, with the number of kg/m3.